Which of the following is an example of an equation with no solution?(1 point)

Question

Responses
1. 3x+4=3x+4
2. 3x+4=4x+3
3. 3x+4=3x+3
4. 4x+3=3x+3
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 1

The equation with no solution is:

3. $3x+4=3x+3$

To explain: when you subtract $3x$ from both sides, you get $4=3$, which is a false statement and indicates that there is no solution.

Answer 2

Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
1. 4x+3=4x+3
2. 3x+4=3x+4
3. 3x+4=3x+3
4. 3x+4=4x+3
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 3

The equation with exactly one solution is:

4. $3x+4=4x+3$

To explain: When you solve this equation, you move the terms involving $x$ to one side and the constants to the other:

1. Subtract $3x$ from both sides: $4=x+3$
2. Subtract $3$ from both sides: $1=x$

This gives you a single solution, $x=1$. The other options either have no solution or infinitely many solutions.

Answer 4

Solve for x to determine if the equation has one, none, or infinite solutions. 3(x+2)−6=3x (1 point)

Responses
1. The equation has infinite solutions.
2. The equation has no solution.
3. The equation has one solution: x=3.
4. The equation has one solution: x=−3.
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 5

Let's solve the equation $3(x+2)-6=3x$.

1. Distribute on the left side: $$3x+6-6=3x$$ This simplifies to: $$3x=3x$$

At this point, since both sides of the equation are the same, this means that the equation holds true for all values of $x$.

Thus, the equation has infinite solutions.

The correct answer is: 1. The equation has infinite solutions.

Answer 6

Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15 (1 point)
Responses
1. The equation has one solution: x=0.
2. The equation has infinite solutions.
3. The equation has no solution.
4. The equation has one solution: x=−10.
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 7

Let's solve the equation $4x=3(x+5)-15$.

1. Distribute the $3$ on the right side: $$4x=3x+15-15$$ This simplifies to: $$4x=3x$$

2. Subtract $3x$ from both sides: $$4x-3x=0$$ This gives: $$x=0$$

Since we have found a specific solution for $x$, the equation has one solution.

The correct answer is: 1. The equation has one solution: x=0.

Answer 8

Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6 (1 point)
Responses
1. The equation has one solution: x=6.
2. The equation has no solution.
3. The equation has one solution: x=10.
4. The equation has infinite solutions.
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 9

Let's solve the equation $5(2x+2)-7x=3x+6$.

1. Distribute the $5$ on the left side: $$10x+10-7x=3x+6$$ This simplifies to: $$3x+10=3x+6$$

2. Now, subtract $3x$ from both sides: $$10=6$$

This results in a false statement, which indicates that there are no solutions to the equation.

The correct answer is: 2. The equation has no solution.

Answer 10

Thanks Mini Bot all of these answers are right!

Answer 11

You're welcome! I'm glad to hear that the answers were helpful. If you have any more questions or need further assistance, feel free to ask!